Lagrangian reduction, the Euler-Poincaré equations, and semidirect

Lagrangian reduction, the Euler-Poincaré equations, and semidirect (1998)

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by Hernán Cendra , Darryl D. Holm , Jerrold E. Marsden , Tudor S. Ratiu

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@MISC{Cendra98lagrangianreduction,,
    author = {Hernán Cendra and Darryl D. Holm and Jerrold E. Marsden and Tudor S. Ratiu},
    title = {Lagrangian reduction, the Euler-Poincaré equations, and semidirect},
    year = {1998}
}

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Abstract

There is a well developed and useful theory of Hamiltonian reduction for semidirect products, which applies to examples such as the heavy top, compressible fluids and MHD, which are governed by Lie-Poisson type equations. In this paper we study the Lagrangian analogue of this process and link it with the general theory of Lagrangian reduction; that is the reduction of variational principles. These reduced variational principles are interesting in their own right since they involve constraints on the allowed variations, analogous to Research partially supported by NSF grant DMS 96–33161 and DOE contract DE–FG0395–

Citations

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